課程名稱 (中文) 隨機過程 (英文) Random Variable & Stochastic Process 開課單位 電機工程學系 課程代碼 E4070 授課教師 龔宗鈞 學分數 3.0 必/選修 選修 開課年級 大四 先修科目或先備能力：工程數學(微積分、矩陣、富氏分析) 課程概述與目標：使學生了解隨機變數與隨機過程之數學理論與物理觀念，並能夠應用於系統上之分析與設計。 教科書 作者 : Peyton Z. Peebles, Jr. 書名 : Probability, Random Variables and Random Signal Principles 出版社 : McGraw Hill(ISBN 0-07-118181-4) 參考教材
 課程大綱 學生學習目標 單元學習活動 學習成效評量 備註 週 單元主題 內容綱要 1 Probability 1. Probability Introduced Through Sets and Relative Frequency 2. Joint and Conditional Probability To understand: experiments and sample spaces, discrete and continuous sample spaces, events, probability definition and axioms, joint and conditional probability, Bayes' theorem. 講授 2 Probability 1. Independent Events 2. Combined Experiments 3. Bernoulli Trials To understand: two events, multiple events, properties of independent events, combined sample space, events on the combined sample space, Bernoulli trials. 講授 3 The Random Variable 1. The Random Variable Concept 2. Distribution Function 3. Density Function To understand: definition of random variable, conditions for a function to be a random variable, discrete and continuous random variable, mixed random variable, distribution function, density function. 講授 4 The Random Variable 1. The Gaussian Random Variable 2. Other Distribution and Density Examples 3. Conditional Distribution and Density Function To understand: the Gaussian random variable, binomial distribution, Possion distribution, uniform distribution, conditional distribution, conditional density function. 講授 作業 5 Operations on One Random Variable (RV) 1. Expection 2. Moments To understand: expected value of a RV, expected value of a function of a RV, moments about the origin, central moments, variance and skew, Chebychev's inequality. 講授 6 Operations on One Random Variable (RV) 1. Transformations of a Random Variable To understand: monotonic transformations of a continuous RV, nonmonotonic transformations of a continuous RV, transformation of a discrete RV. 講授 平時考 7 Multiple Random Variables 1. Vector Random Variables 2. Joint Distribution and Its Properties To understand: joint distribution function and its properties, marginal distribution functions. 講授 作業 8 Multiple Random Variables 1. Joint Density and Its Properties 2. Conditional Distribution and Density To understand: joint density function and its properties, marginal density functions, conditional distribution and density. 講授 9 Random Variables 1. Probability 2. Random Variables 3. Operations on One Random Variable 4. Multiple Random Variables To understand: 1. Probability 2. Random Variables 3. Operations on One Random Variable 4. Multiple Random Variables 期中考 10 Multiple Random Variables 1. Statistical Independence 2. Distribution and Density of a Sum of RVs 3. Central Limit Theorem To understand: statistical independence of RVs, distribution and density of a sum sum of two RVs, central limit theorem. 講授 11 Operations on Multiple Random Variables 1. Expected Value of a Function of Random Variables 2. Joint Characteristic Functions 3. Joint Gaussian Random Variables To understand: joint moments about the origin, joint characteristic functions, joint Gaussian RVs. 講授 12 Operations on Multiple Random Variables 1. Transformations of Multiple Random Variables 2. Sampling and Some Limit Theorems To understand: transformations of multiple RVs, sampling and some limit theorems. 講授 13 Random Processes-Temporal Characteristics 1. The Random Process Concept 2. Stationarity and Independence To understand: classification of processes, statistical independence, first-order stationary process, second-order and wide-sense stationarity, N-order and strict-sense stationarity, time average and ergodicity. 講授 作業 14 Random Processes-Temporal Characteristics 1. Correlation Functions 2. Gaussian Random Processes To understand: autocorrelation function and its properties, cross-correlation function and its properties, covariance functions. 講授 平時考 15 Random Processes-Spectral Characteristics 1. Power Density Spectrum and Its Properties 2. Relationship between Power Spectrum and Autocorrelation Function 3. Cross-Power Density Spectrum and Its Properties To understand: the power density spectrum and its properties, bandwidth of the power density spectrum, relationship between power spectrum and autocorrelation function, the cross-power density spectrum and its properties. 講授 16 Random Processes-Spectral Characteristics 1. Power Spectrum for Discrete-Time Processes and Sequences 2. Some Noise Definitions To understand: discrete-time processes, discrete-time sequences, white noise and colored noise. 講授 作業 17 Linear Systems with Random Inputs 1. Linear System Fundamentals 2. Random Signal Response of Linear System 3. Spectral Characteristics of System Response To understand: mean and mean-squared value of system response, autocorrelation function of response, cross-correlation functions of input and output, power density spectrums of response, cross-power density spectrums of input and output. 講授 平時考 18 Random Processes-Spectral Characteristics 1. Random Processes-Temporal Characteristics 2. Random Processes-Spectral Characteristics 3. Linear Systems with Random Inputs To undserstand: random processes-temporal characteristics, random processes-spectral characteristics, linear systems with random inputs. 期末考
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